An omega-type energy filter (.OMEGA.-filter) or alpha-type energy filter (.alpha.-filter) is combined with a transmission electron microscope and used to create an image from only electrons of a certain energy contained in an electron beam that have passed through a specimen.
FIG. 6 shows a conventional structure of an .OMEGA.-filter. This filter is composed of four magnets M.sub.1, M.sub.2, M.sub.3, and M.sub.4 that are excited with currents i.sub.1, i.sub.2, i.sub.3, and i.sub.4, respectively, supplied from power supplies P.sub.1, P.sub.2, P.sub.3, and P.sub.4, respectively.
The direction of the magnetic fields produced by the magnets M.sub.1 and M.sub.4 is vertical to the plane of the paper and directed downward (indicated by ). The direction of the magnetic fields developed by the magnets M.sub.2 and M.sub.3 are vertical to the plane of the paper and directed upward (indicated by .circle-w/dot.). The center orbits drawn by electrons having a certain energy (velocity v) in passing through the magnets M.sub.1, M.sub.2, M.sub.3, and M.sub.4 have radii r.sub.1, r.sub.2, r.sub.3, and r.sub.4, respectively. This .OMEGA.-filter is inserted in the imaging lens system of an electron microscope. Electrons transmitted through the specimen and having different energies enter the .OMEGA.-filter. Of these electrons, only those having a certain energy pass through the filter and are returned to the imaging lens system. The radius r.sub.1 of the orbit is given by EQU r.sub.1 =mv/eB.sub.1 ( 1)
where m is the mass of the electron, v is the velocity of the electron, e is the charge of the electron, and B.sub.1 is the magnetic flux density of the magnetic field produced by the magnet M.sub.1. Similar relations hold for the radii r.sub.2, r.sub.3, and r.sub.4 of the other orbits. Let B the magnetic flux density of the magnetic field produced by each magnet. As is well known in the art, this magnetic flux density is given by EQU B=.mu.Ni/D (2)
where .mu. is the permeability of vacuum, N is the number of turns, i is the exciting current, and D is the gap in the magnet.
In the structure shown in FIG. 6, it is assumed that the magnets M.sub.1, M.sub.2, M.sub.3, and M.sub.4 are identical in gap length. Exciting currents supplied to the coils are given by EQU i.sub.1 =T/r.sub.1 N.sub.1 ( 3) EQU i.sub.2 =T/r.sub.2 N.sub.2 ( 4) EQU i.sub.3 =T/r.sub.3 N.sub.3 ( 5) EQU i.sub.4 =T/r.sub.4 N.sub.4 ( 6)
Thus, only the electrons that are contained in the incident electron beam and have a certain energy (velocity v) move in an orbit O like the letter .OMEGA. and emerge as outgoing electrons. In Eqs. (3)-(6) above, T is a common coefficient determined by the velocity v of the electrons moving in the orbit 0 and by the gap length D of the magnets M.sub.1, M.sub.2, M.sub.3, and M.sub.4, and is given by EQU T=mvD/e.mu. (7)
where .mu. is the permeability of vacuum. N.sub.1, N.sub.2, N.sub.3, and N.sub.4 are the numbers of turns of the coils of the magnets M.sub.1, M.sub.2, M.sub.3, and M.sub.4, respectively.
FIG. 7 shows an example of .alpha.-filter configuration. The illustrated .alpha.-filter is equipped with three magnets M.sub.11, M.sub.12, and M.sub.13, which are excited with currents i.sub.11, i.sub.12, and i.sub.13, respectively, supplied from power supplies P.sub.11, P.sub.12, and P.sub.13, respectively. Magnetic fields produced by these three magnets M.sub.11, M.sub.12, and M.sub.13 are all directed vertically downward from the plane of the paper.
In this structure, only the electrons of the incident electron beam having a certain energy (velocity v) move in a substantially .alpha.-shaped orbit O and leave the filter. The center orbits described by the electrons having the certain energy (velocity v) in passing through the magnets M.sub.11, M.sub.12 and M.sub.13 have radii r.sub.11, r.sub.12, and r.sub.13, respectively.
In the prior art .OMEGA.-filter, one power supply is provided for each one magnet as shown in FIG. 6. Where electrons having a certain energy (velocity v) are selected, the operator must adjust the 4 power supplies to satisfy Eqs. (3)-(6) above. These operations are very cumbersome and laborious to perform. The .alpha.-filter has similar disadvantages. That is, the operator normally must adjust the exciting currents fed to the three magnets so that electrons of a certain energy (velocity v) pass through the magnets.